Regression calibration [1]}, [2]} models the relationship between \(Y_i\)  and \(\lbrace X_i^*, Z_i\rbrace \)  based on an assumed model between \(Y_i\)  and \(\lbrace X_i,Z_i\rbrace \)  and a model between \(X_i\)  and \(\lbrace X_i^*,Z_i\rbrace \) . While there exist many specific implementations of regression calibration, we consider the best linear unbiased prediction (BLUP) technique [3]}.
